CART: Constant Aspect Ratio Tiling

International audienceParametric tiling is a well-known transformation which is widely used to improve locality, parallelism and granularity. However, parametric tiling is also a non-linear transformation and this prevents polyhedral analysis or further polyhedral transformation after parametric tiling. It is therefore generally applied during the code generation phase. In this paper, we present a method to stay polyhedral in a special case of parametric tiling, where all the dimensions are tiled and all the tile sizes are constant multiples of a single tile size parameter. We call this Constant Aspect Ratio Tiling. We show how to mathematically transform a polyhedron and an affine function into their tiled counterpart, which are the two main operations needed in such transformation